SAT Test Prep

CHAPTER 6WHAT THE SAT MATH IS REALLY TESTING

Lesson 5: Connecting to Knowledge

Know What You Need

Some SAT math questions require you to use special formulas or know the definitions of special terms. Fortunately, you won’t need to memorize very many formulas (none of that trig stuff, for instance), and some of the most important ones are given to you right on the test!

Reference Information

Every SAT math section gives you this reference information. Check it out and use it when you need it.

The arc of a circle measures 360°.

Every straight angle measures 180°.

The sum of the measures of the angles in a triangle is 180°.

Memorize the Key Formulas They DON’T Give You

It’s awfully nice of the SAT to give you those formulas, but those are not quite all you’ll need. Fortunately, we can fit the other key formulas on a single page. Here they are:

Rate formula (Chapter 9, Lesson 4):

Distance (or work) = rate ×time

Average (arithmetic mean) formulas (Chapter 9 Lesson 2):

Slope formula (Chapter 10, Lesson 4):

Midpoint formula (Chapter 10, Lesson 4):

Percent change formula (Chapter 7, Lesson 5):

Memorize the Key Definitions

You’ll also want to memorize the definitions of some key terms that show up often:

Mode = the number that appears the most frequently in a set. Remember that mode and most both begin with mo (Chapter 9, Lesson 2). Median = the “middle number” of a set of numbers when they are listed in order. If there are an even number of numbers, the median is the average of thetwo middle numbers (Chapter 9, Lesson 2).

Remainder = the whole number left over when one whole number has been divided into another whole number a whole number of times (Chapter 7, Lesson 7).

Absolute value = the distance a number is from 0 on the number line (Chapter 8, Lesson 6). Prime number = an integer greater than 1 that is divisible only by itself and 1 (Chapter 7, Lesson 7).

Factor = a number or expression that is part of a product. (Product = result of a multiplication.)

Concept Review 5: Connecting to Knowledge

Write out each formula, theorem, definition, or property.

1. The Pythagorean theorem

2. The zero product property

3. The parallel lines theorem

4. The rate formula

5. The average (arithmetic mean) formula

6. The definition of the median

7. The definition of the mode

8. The circumference formula

9. The circle area formula

10. The triangle area formula

SAT Practice 5: Connecting to Knowledge

1. If x is the average (arithmetic mean) of k and 10, and y is the average (arithmetic mean) of k and 4, what is the average of x and y, in terms of k?

(D) 7k

(E) 14k

2. If, on average, x cars pass a certain point on a highway in y hours, then, at this rate, how many cars should be expected to pass the same point in z hours?

(A) xyz

3. A straight 8-foot board is resting on a rectangular box that is 3 feet high, as shown in the diagram above. Both the box and the board are resting on a horizontal surface, and one end of the board rests on the ground 4 feet from the edge of the box. If h represents the height, in feet, of the other end of the board from the top of the box, what is h?

Key formula(s):

Key formula(s):

Key formula(s):

Answer Key 5: Connecting to Knowledge

Concept Review 5

1. The Pythagorean theorem: In a right triangle, if c is the length of the hypotenuse and a and b are the lengths of the two legs, then (Chapter 10, Lesson 3).

2. The zero product property: If a set of numbers has a product of zero, then at least one of the numbers is zero. Conversely, if zero is multiplied by any number, the result is zero (Chapter 8, Lesson 5).

3. The parallel lines theorem: If a line cuts through two parallel lines, then all acute angles formed are congruent, all obtuse angles formed are congruent, and any acute angle is supplementary to any obtuse angle (Chapter 10, Lesson 1).

6. The definition of the median: The “middle number” of a set of numbers when they are listed in order. If there are an odd number of numbers, the median is the “middle number,” and if there are an even number of numbers, it is the average of the two middle numbers (Chapter 9, Lesson 2).

7. The definition of the mode: The number that appears the most frequently in a set (Chapter 9, Lesson 2).

1.C Key formula: Average = sum number of things. So if x is the average of k and 10, then And if y is the average of k and 4, then The average of x and y, then, is

2.D Key formulas: Number of cars = rate ×time, and Since x is the number of cars and y is the time in hours, the rate is x/y cars per hour. Using the first formula, then, the number of cars that would pass in z hours is

You should notice, too, that simply plugging in values for x, y, and z can make the problem easier to think about. Say, for instance, that cars pass every hours. In hours, then, it should be clear that 20 cars should pass by. Plugging these numbers into the choices, you will see that (D) is the only one that gives an answer of 20.

3.1.8 Key formula: The Pythagorean theorem: . Key theorem: In similar triangles, corresponding sides are proportional. Notice that the figure has two right triangles, and they are similar. The hypotenuse of the bottom triangle is 5 because . Therefore, the hypotenuse of the top triangle is . Since the two triangles are similar, the corresponding sides are proportional: